Note that \(Q^{\text{ion}}_\mathrm {\mathfrak {e}}\)  corresponds to the optically thin radiative losses term which involve hydrogen and helium ionization potential coefficients, as described by [1]}, [2]}. The Spitzer term is anisotropic with respect to the magnetic field and is identical to the definition from [3]}, [4]}. The heating term due to viscous effects \(Q_\mathrm {\mathfrak {a}\mathcal {I}}^{\tau }\)  is derived from the viscous terms in momentum equations \(\tau _{\mathfrak {a}\mathcal {I}}\)  leading to a similar expression introduced by [5]}, [4]} for a single-fluid MHD model.
